228 
MR. S. S. HOUGH ON THE APPLICATION OF HARMONIC 
whence 
pjcr = ’18093, 
yj9 = 
uJy = 
gjg = 
9%!9 = 
9iJ9 =■- 
•89144 
•93969 
•95825 
•96807 
•97415 
9iil9 = 
9iJ9 = 
9iJ9 = 
9iil9 = 
9%^\9 = 
•97829 
•98128 
•98355 
•98533 
•98676 
the values of g^lg approximating closer and closer to unity as n increases. 
Next take hgjiora^ = which corresponds to a depth of -^y-Q of the earth’s 
radius, or about 7260 feet. With this value of the depth we find 
L = 0-3 (£. - ’) + -0^295, 
L = o (£= - ') + -002482, 
= 6-7 (£=-t)--0”835, 
L = sb (£=-i)--04^1«4, 
L-=lo!u(4b-l)--019777, 
L,3 
L 
L 
L 
12. 
13 
V4a)-’ 
1 
~ 14. 
15 
Ua)2 
1 
“ 16. 
17 
\4&)2 
1 
~ 18. 
19 
\4:C^ 
1 
fX^ 
“ 20. 
21 ' 
V4a)2 
14 — 
16 
18 — 
•021237, 
•022143, 
•022746, 
•023168, 
•023476. 
Introduce for brevity the notation 
K.= 
_ {-In + 1) (291 + 3)2 (2i4 + 5) {2n - 3) {2n - l)^ (2ft + 1) 
^7^9 
L. 
1 
—2 
1 
- ... - U 
{2n - -S){2n - If {2n + 1) i2n + 1) {2n + 3f {-2n + 5) 
L,j +2 
— ad inf. 
The period-equation (29) may then be written 
L/i H«_2 ^« + 2 — fi. 
Suppose now that X^/4aj^ has a value found by equating to zero one of the quantities 
say for example Lg; putting Lg = 0 , we obtain with the numerical values given 
above . 
^,= 2-23726, 
